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Juan Wang - One of the best experts on this subject based on the ideXlab platform.
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Shakedown of asphalt pavements considering temperature effect
International Journal of Pavement Engineering, 2020Co-Authors: S Liu, Juan Wang, Dariusz Wanatowski, Nick Thom, James GrenfellAbstract:Shakedown limit has been perceived as a useful guidance in pavement structure design against rutting. However, temperature, as one key factor influencing the Shakedown limit of asphalt pavements, h...
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Shakedown Limits of Slab Track Substructures and Their Implications for Design
Direct Methods, 2020Co-Authors: Juan Wang, Shu LiuAbstract:This paper presents an approach to Shakedown of slab track substructures subjected to train loads. The train load is converted into a distributed moving load on the substructure surface using a simplified track analysis. Based on the lower-bound dynamic Shakedown theorem, Shakedown solutions for the slab track substructures are obtained over a range of train speeds between zero and the critical speed of the track. It is found the Shakedown limit is largely influenced by the ratio of layer elastic moduli and the ratio of train speed to critical speed rather than their absolute values. An attenuation factor, as a function of the critical speed and the friction angle of subsoil, is proposed to effectively obtain the Shakedown limit of the slab track substructure at any train speed. In light of the Shakedown solutions, improvements to the existing design and analysis approaches are also suggested.
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the influence of traffic moving speed on Shakedown limits of flexible pavements
International Journal of Pavement Engineering, 2019Co-Authors: Jiangu Qian, Juan Wang, Yonggang Wang, Maosong HuangAbstract:AbstractShakedown theory is often used to analyse elastic–plastic responses of structures subjected to variable or repeated loads. In pavement engineering, it has been used to predict the maximum admissible load (termed as ‘Shakedown limit’) against excessive rutting in flexible pavements. Pavement Shakedown analysis, which involves the calculation of the pavement Shakedown limit, usually utilised elastic stresses induced by a static wheel load and therefore neglected any possible dynamic responses. This paper will, for the first time, evaluate the dynamic effect of the moving load on the Shakedown limit of flexible pavement. A numerical approach is developed based on a recent lower bound method for solving the pavement Shakedown problem. The dynamic responses of elastic stresses to the moving traffic loads are computed using finite element method in which infinite elements are used for boundaries. Shakedown limits for a single subgrade layer and a pavement-subgrade system under traffic loads at various s...
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Recent Progress on Lower-Bound Shakedown Analysis of Road Pavements
Advances in Direct Methods for Materials and Structures, 2017Co-Authors: Juan Wang, S LiuAbstract:Shakedown theory has been recognised as a more rational basis for structural design of flexible road pavements. A lower-bound Shakedown approach, which aims to find the maximum design load of a pavement structure, was developed by the University of Nottingham, that forms part of efforts among other researchers’ in applying Shakedown theory in pavement designs. The lower-bound Shakedown solutions were consistent with existing Shakedown solutions assuming that the materials are isotropic and homogeneous following an associated plastic flow rule. Recently, this lower-bound approach was further developed to consider more realistic cases. Both two-dimensional and three-dimensional Shakedown analyses were carried out taking into account cross-anisotropic or heterogeneous materials, the properties of which were programmed into a finite element software ABAQUS. For pavement materials obeying a non-associated flow rule, the corresponding two-dimensional lower-bound Shakedown limits were also estimated by extending the lower-bound Shakedown approach. A numerical step-by-step approach was also applied to address the non-associated problems and obtained similar results. Through these studies, influences of the original assumptions on the Shakedown-based pavement designs can be assessed.
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Shakedown solutions for pavements with materials following associated and non-associated plastic flow rules
Computers and Geotechnics, 2016Co-Authors: Shu Liu, Juan Wang, Dariusz WanatowskiAbstract:Existing lower-bound Shakedown solutions for pavement problems are generally obtained by assuming that materials obey an associated flow rule, whereas plasticity of real materials is more inclined to a non-associated flow. In this paper, a numerical step-by-step approach is developed to estimate Shakedown limits of pavements with Mohr–Coulomb materials. In particular, influences of a non-associated flow rule on the Shakedown limits are examined by varying material dilation angle in the numerical calculations. It is found that the decrease of dilation angle will lead to accelerated reduction of pavement Shakedown limits, and the reduction is most significant when the material friction angle is high. Furthermore, existing lower-bound Shakedown solutions for pavements are extended, in an approximate manner, to account for the change of material dilation angle and the Shakedown results obtained in this way agree well with those obtained through the numerical step-by-step approach. An example of pavement design using Shakedown theory is also presented.
Shu Liu - One of the best experts on this subject based on the ideXlab platform.
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Shakedown Limits of Slab Track Substructures and Their Implications for Design
Direct Methods, 2020Co-Authors: Juan Wang, Shu LiuAbstract:This paper presents an approach to Shakedown of slab track substructures subjected to train loads. The train load is converted into a distributed moving load on the substructure surface using a simplified track analysis. Based on the lower-bound dynamic Shakedown theorem, Shakedown solutions for the slab track substructures are obtained over a range of train speeds between zero and the critical speed of the track. It is found the Shakedown limit is largely influenced by the ratio of layer elastic moduli and the ratio of train speed to critical speed rather than their absolute values. An attenuation factor, as a function of the critical speed and the friction angle of subsoil, is proposed to effectively obtain the Shakedown limit of the slab track substructure at any train speed. In light of the Shakedown solutions, improvements to the existing design and analysis approaches are also suggested.
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dynamics Shakedown analysis of slab track substructures with reference to critical speed
Soil Dynamics and Earthquake Engineering, 2018Co-Authors: Jua Wang, Shu Liu, Wenbo YangAbstract:Abstract In this paper, the long-term response of a slab track substructure to moving train loads as well as its relation with critical speed is evaluated using lower-bound dynamic Shakedown analysis. The train loads are converted into a distributed moving load on the substructure surface using a simplified track analysis. The Mohr-Coulomb criterion is adopted for substructure materials. By conceiving a self-equilibrated and time-independent critical residual stress field and calculating velocity-dependent fictitious elastic stress fields, dynamic Shakedown solutions for the substructures are obtained. The Shakedown limits for homogenous and layered substructures are examined considering various train speeds, elastic moduli, friction angles and layer thicknesses. Meanwhile, the critical speeds of the substructures are investigated, which are consistent with literatures. It is found the friction angle will affect the Shakedown limit but not the critical speed. The change of the Shakedown limit from the static solution relies on the ratio of layer elastic moduli and the ratio of train speed to critical speed rather than their absolute values. For a typical three-layered substructure, there exists an optimum subgrade layer thickness, as any further increase in the thickness alone will not improve the Shakedown limit. The safe train load can be expressed as a function of static Shakedown limit and velocity factor.
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Application of Shakedown theory in the structural design of bituminous pavements
2016Co-Authors: Shu LiuAbstract:Excessive rutting, one of the major distress modes of bituminous pavements, is mainly caused by the accumulation of load-induced permanent deformation. However, current pavement design approaches against the excessive rutting are mainly developed using the theory of elasticity. Recently, a new pavement design approach based on the Shakedown concept has attracted lots of attention because it can consider plastic properties of pavement materials. However, most of the existing Shakedown solutions were developed for pavement foundations composed of granular materials and soils. Very limited work has been reported on bituminous pavements. Besides, current studies usually assume homogeneous, isotropic pavement materials obeying an associated plastic flow rule (termed as standard materials in the present study), which may not be realistic for pavement materials. In the present research, a step-by-step numerical approach was used to obtain numerical Shakedown limits of pavement structures under repeated moving loads. Both two-dimensional and three-dimensional problems were considered. It was found that, under the assumption of standard materials, the obtained numerical Shakedown limits and residual stress fields agreed well with the available theoretical data. A static (i.e. lower bound) Shakedown approach for pavements with anisotropic, heterogeneous materials was developed based on Melan’s lower bound theorem and the critical residual stress method of Yu and Wang (2012). The influence of material plastic flow rules on pavement Shakedown limits was also evaluated both numerically and theoretically. It was found that neglect of the inherent material properties (i.e. anisotropy, heterogeneity and non-associated plastic flow) could overestimate the real Shakedown limits of bituminous pavements. A series of tests were conducted to validate the Shakedown concept for the responses of bituminous pavements under traffic loads. Two distinct phenomena corresponding to Shakedown and non-Shakedown were observed. Triaxial tests and uniaxial compression tests were also undertaken to obtain the stiffness and strength parameters, from which the theoretical Shakedown limits can be calculated. Comparison between the experimental results and the theoretical solutions revealed that the current 3D Shakedown approach for standard materials may overestimate capacities of bituminous pavements. Finally, the lower bound Shakedown approach was employed to design a typical bituminous pavement. A direct comparison was made between the Shakedown-based design and the current UK design method. It demonstrated that the Shakedown-based design for bituminous pavements can be conducted considering the maximum contact pressure and a relatively high air temperature.
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Shakedown solutions for pavements with materials following associated and non-associated plastic flow rules
Computers and Geotechnics, 2016Co-Authors: Shu Liu, Juan Wang, Dariusz WanatowskiAbstract:Existing lower-bound Shakedown solutions for pavement problems are generally obtained by assuming that materials obey an associated flow rule, whereas plasticity of real materials is more inclined to a non-associated flow. In this paper, a numerical step-by-step approach is developed to estimate Shakedown limits of pavements with Mohr–Coulomb materials. In particular, influences of a non-associated flow rule on the Shakedown limits are examined by varying material dilation angle in the numerical calculations. It is found that the decrease of dilation angle will lead to accelerated reduction of pavement Shakedown limits, and the reduction is most significant when the material friction angle is high. Furthermore, existing lower-bound Shakedown solutions for pavements are extended, in an approximate manner, to account for the change of material dilation angle and the Shakedown results obtained in this way agree well with those obtained through the numerical step-by-step approach. An example of pavement design using Shakedown theory is also presented.
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Shakedown of Layered Pavements under Repeated Moving Loads
Pavement Materials Structures and Performance, 2014Co-Authors: Shu Liu, Juan Wang, Dariusz WanatowskiAbstract:In recent years, Shakedown theory has been suggested as a more rational theoretical foundation for pavement structural design. This paper suggests a numerical approach to find Shakedown load limit of layered pavements based on an investigation of residual stress field, which plays an important role in helping the structure to reach the Shakedown status. A finite element model is established for pavement structures under repeated moving surface loads, where the Mohr-Coulomb yield criterion with associated plastic flow is assumed to capture the plastic behaviour of pavement materials. A criterion based on static Shakedown theorem is suggested to distinguish Shakedown and non-Shakedown status of pavement structures subjected to different magnitudes of loads, thereby achieving a numerical Shakedown limit. Comparisons between the numerical Shakedown limits and theoretical Shakedown limits of Wang and Yu (2013a) show good agreement. Investigation of the development of residual stresses in layered pavements also provides deep insight to the application of Shakedown theory. In addition, the proposed approach can be easily extended to pavement materials following non-associated plastic flow rule.
Pham Duc Chinh - One of the best experts on this subject based on the ideXlab platform.
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Shakedown theory for elastic-perfectly plastic bodies revisited
International Journal of Mechanical Sciences, 2003Co-Authors: Pham Duc ChinhAbstract:Abstract Yield criteria for elastic-perfectly plastic solids, in particular, the Mises and Tresca ones, permit unlimited hydrostatic stresses, leading to some singularity in the classical Melan–Koiter Shakedown theory. Classical Shakedown theory is re-examined regarding this problem. It is shown that the complete proofs of both static and kinematic theorems require restrictions on the hydrostatic stresses. A modified Shakedown kinematic theorem using a fictitious material that can yield in bulk tension and compression has been constructed for subsequent treatment of real engineering materials, which cannot yield but fail under high hydrostatic stresses. The kinematic theorem should have vanishing hydrostatic plastic strain rate solution for the safety of the body against hydrostatic fracture. In this way, the modified kinematic formulation including the limits on hydrostatic stresses are suggested for application. The modifications are also naturally added into the plastic limit theory, which is a limiting case of the Shakedown one. Also in the paper, the kinematic approach is used to deduce some simplified estimates for specific non-Shakedown collapse modes of elastic plastic structures.
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Shakedown kinematic theorem for elastic perfectly plastic bodies
International Journal of Plasticity, 2001Co-Authors: Pham Duc ChinhAbstract:Abstract The classical Shakedown kinematic theorem due to Koiter for elastic–perfectly plastic bodies is re-examined and divided into separated Shakedown and nonShakedown theorems. While the Shakedown theorem is based on the set of Koiter's plastic strain rate cycles, the non-Shakedown one involves a broader set of admissible plastic strain rate cycles, the end-cycle accumulated strains of which are deviatoric parts of compatible strain fields. For certain broad classes of practical problems the two statements are unified to yield the unique theorem in Koiter's sense.
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Shakedown kinematic theorem for elastic–perfectly plastic bodies
International Journal of Plasticity, 2001Co-Authors: Pham Duc ChinhAbstract:Abstract The classical Shakedown kinematic theorem due to Koiter for elastic–perfectly plastic bodies is re-examined and divided into separated Shakedown and nonShakedown theorems. While the Shakedown theorem is based on the set of Koiter's plastic strain rate cycles, the non-Shakedown one involves a broader set of admissible plastic strain rate cycles, the end-cycle accumulated strains of which are deviatoric parts of compatible strain fields. For certain broad classes of practical problems the two statements are unified to yield the unique theorem in Koiter's sense.
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Shakedown of bars subjected to cycles of loads and temperature
International Journal of Solids and Structures, 1993Co-Authors: Pham Duc ChinhAbstract:Abstract A new mathematical method is developed to study the Shakedown of bar systems subjected to cycles of loads and temperature allowing for temperature dependence of the yield stresses. For a parallel bar system constrained to have equal displacements at the ends, the Shakedown factor is obtained in an explicit analytical form. The possible inadaptation modes of incremental collapse (structural ratchetting) and alternating plasticity (low cycle fatigue) on the boundary of the Shakedown domain are determined.
Xi-qiao Feng - One of the best experts on this subject based on the ideXlab platform.
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On Shakedown of three-dimensional elastoplastic strain-hardening structures
International Journal of Plasticity, 1996Co-Authors: Xi-qiao FengAbstract:The present article considers the Shakedown problem of structures made of either kinematic or mixed strain-hardening materials. Some basic and useful Shakedown properties of elastoplastic strain-hardening structures are proved mathematically. It is impossible for a kinematic strain-hardening structure to be involved in incremental plastic collapse, and so its only possible failure mode is that of alternating plasticity. A time-independent self-equilibrium stress field has no influence on the Shakedown of a kinematic strain-hardening structure although it contributes to the magnitude of plastic deformation. The sufficient Shakedown conditions for either kinematic or mixed strain-hardening structures are deduced, from which the lower bound of Shakedown load domain can be obtained via a mathematical programming problem. It should be pointed out that, to guarantee the safety of an elastoplastic strain-hardening structure, the damage analysis is also necessary to determine the maximum load factor the structure can bear. The Shakedown analysis of strain-hardening structures can be simplified by the conclusions obtained in this article, as is illustrated by two simple examples.
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Structures at Shakedown
1994Co-Authors: Xi-qiao FengAbstract:In this paper, a Shakedown theory for plastic-damaged structures is pre- sented. Damage mechanics and Shakedown theory are closely related to each other in some aspects. The damage of materials may change their mechanical properties and as well as the Shakedown load domains of structures. Here the damage variable is proposed as the failure criterion of ductile structures at Shakedown. Based on an elastic perfect- ly—plastic damage model, an upper bound on local damage of structures is given via a mathematical programming. The suggested method is illustrated by an example of thick- walled cylindrical tube.
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An Upper Bound on Damage of Elastic-Plastic Structures at Shakedown
International Journal of Damage Mechanics, 1994Co-Authors: Xi-qiao FengAbstract:In this paper, a Shakedown theory for plastic-damaged structures is pre sented. Damage mechanics and Shakedown theory are closely related to each other in some aspects. The damage of materials may change their mechanical properties and as well as the Shakedown load domains of structures. Here the damage variable is proposed as the failure criterion of ductile structures at Shakedown. Based on an elastic perfect ly—plastic damage model, an upper bound on local damage of structures is given via a mathematical programming. The suggested method is illustrated by an example of thick- walled cylindrical tube.
Kristian Krabbenhøft - One of the best experts on this subject based on the ideXlab platform.
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bounds for Shakedown of cohesive frictional materials under moving surface loads
International Journal of Solids and Structures, 2008Co-Authors: Jidong Zhao, Scott W. Sloan, Andrei V. Lyamin, Kristian KrabbenhøftAbstract:In this paper, Shakedown of a cohesive-frictional half space subjected to moving surface loads is investigated using Melan’s static Shakedown theorem. The material in the half space is modelled as a Mohr–Coulomb medium. The sliding and rolling contact between a roller and the half space is assumed to be plane strain and can be approximated by a trapezoidal as well as a Hertzian load distribution. A closed form solution to the elastic stress field for the trapezoidal contact is derived, and is then used for the Shakedown analysis. It is demonstrated that, by relaxing either the equilibrium or the yield constraints (or both) on the residual stress field, the Shakedown analysis leads to various bounds for the elastic Shakedown limit. The differences among the various Shakedown load factors are quantitatively compared, and the influence of both Hertzian and trapezoidal contacts for the half space under moving surface loads is studied. The various bounds and Shakedown limits obtained in the paper serve as useful benchmarks for future numerical Shakedown analysis, and also provide a valuable reference for the safe design of pavements. 2008 Elsevier Ltd. All rights reserved.
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Bounds for Shakedown of cohesive-frictional materials under moving surface loads
International Journal of Solids and Structures, 2008Co-Authors: Jidong Zhao, Scott W. Sloan, Andrei V. Lyamin, Kristian KrabbenhøftAbstract:In this paper, Shakedown of a cohesive-frictional half space subjected to moving surface loads is investigated using Melan’s static Shakedown theorem. The material in the half space is modelled as a Mohr–Coulomb medium. The sliding and rolling contact between a roller and the half space is assumed to be plane strain and can be approximated by a trapezoidal as well as a Hertzian load distribution. A closed form solution to the elastic stress field for the trapezoidal contact is derived, and is then used for the Shakedown analysis. It is demonstrated that, by relaxing either the equilibrium or the yield constraints (or both) on the residual stress field, the Shakedown analysis leads to various bounds for the elastic Shakedown limit. The differences among the various Shakedown load factors are quantitatively compared, and the influence of both Hertzian and trapezoidal contacts for the half space under moving surface loads is studied. The various bounds and Shakedown limits obtained in the paper serve as useful benchmarks for future numerical Shakedown analysis, and also provide a valuable reference for the safe design of pavements
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Bounds to Shakedown Loads for a Class of Deviatoric Plasticity Models
Computational Mechanics, 2006Co-Authors: Kristian Krabbenhøft, Andrei V. Lyamin, Scott W. SloanAbstract:The problem of estimating bounds to Shakedown loads for problems governed by a class of deviatoric plasticity models including those of Hill, von Mises, and Tresca is addressed. Assuming that an exact elastic solution is available, an upper bound to the elastic Shakedown multiplier can be obtained relatively easily using the plastic Shakedown theorem. A procedure for computing this upper bound for arbitrary load domains is presented. A number of problems are then examined and it is found that the elastic Shakedown factor is given as the minimum of the plastic Shakedown factor and the classical limit load factor. Finally, some exact solutions to a number of two dimensional problems are given.
